The last years have seen striking improvements on Vaisman's question about existence of locally conformally K\"ahler (lcK) metrics on compact complex surfaces. The aim of this paper is two-fold. We review results of different authors which, for all known examples of compact complex surfaces, give a complete answer to the Vaisman's question. We also point out a relation between lcK surfaces and generalized K\"ahler geometry in four-dimension and prove a new result concerning %generalized K\"ahler structures on Hyperbolic Inoue surfaces. We conclude with a simple observation on a question of Brunella.
Pontecorvo M (2014). On a question of Vaisman concerning complex surfaces. ANNALI DI MATEMATICA PURA ED APPLICATA, 193(5), 1283-1293.
Titolo: | On a question of Vaisman concerning complex surfaces |
Autori: | |
Data di pubblicazione: | 2014 |
Rivista: | |
Citazione: | Pontecorvo M (2014). On a question of Vaisman concerning complex surfaces. ANNALI DI MATEMATICA PURA ED APPLICATA, 193(5), 1283-1293. |
Abstract: | The last years have seen striking improvements on Vaisman's question about existence of locally conformally K\"ahler (lcK) metrics on compact complex surfaces. The aim of this paper is two-fold. We review results of different authors which, for all known examples of compact complex surfaces, give a complete answer to the Vaisman's question. We also point out a relation between lcK surfaces and generalized K\"ahler geometry in four-dimension and prove a new result concerning %generalized K\"ahler structures on Hyperbolic Inoue surfaces. We conclude with a simple observation on a question of Brunella. |
Handle: | http://hdl.handle.net/11590/134701 |
Appare nelle tipologie: | 1.1 Articolo in rivista |